Using a linear approximation, the estimated cube root of 217 is 6.00925.
Given that the number is,
The cube root of 217
Now, for the cube root of 217 using a linear approximation, use differentials.
So, the derivative of the function [tex]f(x) = x^{(1/3)[/tex] at a known point.
Taking the derivative of [tex]f(x) = x^{(1/3)[/tex], we get:
[tex]f'(x) = (\dfrac{1}{3} )x^{-2/3[/tex]
Now, we can choose a point near 217 to evaluate the linear approximation.
Let's use x = 216, which is a perfect cube.
Substituting x = 216 into the derivative, we get:
[tex]f'(216) = (\dfrac{1}{3} )(216)^{-2/3[/tex]
[tex]= 0.00925[/tex]
Next, use the linear approximation formula:
Δy ≈ f'(a)Δx
Since our known point is a = 216 and we want to estimate the cube root of 217,
since 217 - 216 = 1
Hence, Δx = 1
Δy ≈ f'(216)
Δx ≈ 0.00925 × 1
≈ 0.00925
Finally, add this linear approximation to the known value at the known point to get our estimate:
Estimated cube root of 217 ;
f(216) + Δy = 6 + 0.00925
= 6.00925
Therefore, the estimated cube root of 217 is 6.00925.
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Find the square root of (2-36i)/(2+3i)
Answer:
[tex]-8-6i[/tex]
Step-by-step explanation:
[tex]\frac{2-36i}{2+3i} * \frac{2-3 i}{2-3i}[/tex]
-104-78i /13
-8-6i
The square root of (2-36i)/(2+3i) is √(112-66i)/13.
The given expression is [tex]\frac{2-36i}{2+3i}[/tex].
What is the square root?The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.
Multiply both numerator and denominator by 2-3i.
Now, [tex]\frac{2-36i}{2+3i}\times\frac{2-3i}{2-3i}[/tex]
= [tex]\frac{(2-36i)(2-3i)}{(2+3i)(2-3i)}[/tex]
= [tex]\frac{(4-72i+6i-108i^2)}{4-9i^2}[/tex]
= [tex]\frac{(4-66i+108)}{4+9}[/tex]
= [tex]\frac{(112-66i)}{13}[/tex]
Now square root is √(112-66i)/13
Therefore, the square root of (2-36i)/(2+3i) is √(112-66i)/13.
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convert the following to decimal fractions 99 by 5
Answer:
divide 99 by 5
99/5= 19.8
y = (4x+4)^1/2 at x=2
9514 1404 393
Answer:
2√3 ≈ 3.4641016
Step-by-step explanation:
Put the value where the variable is and do the arithmetic.
(4x +4)^(1/2) at x=2 is ...
(4·2 +4)^(1/2) = 12^(1/2) = 2√3 ≈ 3.4641016
__
Additional comment
If you really mean (4x+4)^1/2, then you have 12^1/2 = 12/2 = 6.
If the exponent is 1/2, it needs to be in parentheses.
What is the value of p?
A. 125°
B. 45°
C. 35°
D. 550
Answer:
C- 35 °
Step-by-step explanation:
Interior angle adjacent to 90° angle = 90° (supplementary angles of a line segment).
Interior angle adjacent to 125° angle = 55° (supplementary angles of a line segment).
Sum of two interior angles of the triangle = 55+90 = 145°
∠p = 180° - 145° = 35°
Solve this problem:
5X +8 = 53
5X + 8 = 53
5X = 53 - 8
X = 45 / 5
X = 9
Answer:
X=9
Step-by-step explanation:
5X+8=53
To solve this we need to make X the subject of the equation that means X should be alone on one side of the equation. Taking the following steps
5X=53-8
5X=45
X=45/5
X=9
What is the 11th term of this geometric sequence?: 16384, 8192, 4096, 2048
Answer:
16
Step-by-step explanation:
1) Find out r of the sequence. The first term(a1) is 16384, the second term (a2) is 8192.
8192=16384*r. r= 0.5
2) Use the rule that an=a1*r^(n-1)
a11=a1*r^10
a11= 16384*((0.5)^10)= 16384/ (2^10)=16.
The graph of a linear function is given below. What is the zero of the function?
Answer:
Need to see the problem, but the "zero of the function" is the x value when y=0.
Substitute '0' for y.
Solve for x
Answer: D
Step-by-step explanation:
Two coins are tossed. Assume that each event is equally likely to occur. a) Use the counting principle to determine the number of sample points in the sample space. b) Construct a tree diagram and list the sample space. c) Determine the probability that no tails are tossed. d) Determine the probability that exactly one tail is tossed. e) Determine the probability that two tails are tossed. f) Determine the probability that at least one tail is tossed.
Answer:
(a) 4 sample points
(b) See attachment for tree diagram
(c) The probability that no tail is appeared is 1/4
(d) The probability that exactly 1 tail is appeared is 1/2
(e) The probability that 2 tails are appeared is 1/4
(f) The probability that at least 1 tail appeared is 3/4
Step-by-step explanation:
Given
[tex]Coins = 2[/tex]
Solving (a): Counting principle to determine the number of sample points
We have:
[tex]Coin\ 1 = \{H,T\}[/tex]
[tex]Coin\ 2 = \{H,T\}[/tex]
To determine the sample space using counting principle, we simply pick one outcome in each coin. So, the sample space (S) is:
[tex]S = \{HH,HT,TH,TT\}[/tex]
The number of sample points is:
[tex]n(S) = 4[/tex]
Solving (b): The tree diagram
See attachment for tree diagram
From the tree diagram, the sample space is:
[tex]S = \{HH,HT,TH,TT\}[/tex]
Solving (c): Probability that no tail is appeared
This implies that:
[tex]P(T = 0)[/tex]
From the sample points, we have:
[tex]n(T = 0) = 1[/tex] --- i.e. 1 occurrence where no tail is appeared
So, the probability is:
[tex]P(T = 0) = \frac{n(T = 0)}{n(S)}[/tex]
This gives:
[tex]P(T = 0) = \frac{1}{4}[/tex]
Solving (d): Probability that exactly 1 tail is appeared
This implies that:
[tex]P(T = 1)[/tex]
From the sample points, we have:
[tex]n(T = 1) = 2[/tex] --- i.e. 2 occurrences where exactly 1 tail appeared
So, the probability is:
[tex]P(T = 1) = \frac{n(T = 1)}{n(S)}[/tex]
This gives:
[tex]P(T = 1) = \frac{2}{4}[/tex]
[tex]P(T = 1) = \frac{1}{2}[/tex]
Solving (e): Probability that 2 tails appeared
This implies that:
[tex]P(T = 2)[/tex]
From the sample points, we have:
[tex]n(T = 2) = 1[/tex] --- i.e. 1 occurrences where 2 tails appeared
So, the probability is:
[tex]P(T = 2) = \frac{n(T = 2)}{n(S)}[/tex]
This gives:
[tex]P(T = 2) = \frac{1}{4}[/tex]
Solving (f): Probability that at least 1 tail appeared
This implies that:
[tex]P(T \ge 1)[/tex]
In (c), we have:
[tex]P(T = 0) = \frac{1}{4}[/tex]
Using the complement rule, we have:
[tex]P(T \ge 1) + P(T = 0) = 1[/tex]
Rewrite as:
[tex]P(T \ge 1) = 1-P(T = 0)[/tex]
Substitute known value
[tex]P(T \ge 1) = 1-\frac{1}{4}[/tex]
Take LCM
[tex]P(T \ge 1) = \frac{4-1}{4}[/tex]
[tex]P(T \ge 1) = \frac{3}{4}[/tex]
A sample of 42 observations is selected from one population with a population standard deviation of 3.3. The sample mean is 101.0. A sample of 53 observations is selected from a second population with a population standard deviation of 3.6. The sample mean is 99.0. Conduct the following test of hypothesis using the 0.04 significance level.
H0 : μ1 = μ2
H1 : μ1 ≠ μ2
a. State the decision rule.
b. Compute the value of the test statistic.
c. What is your decision regarding H0?
d. What is the p-value?
Answer:
a)
[tex]|z| < 2.054[/tex]: Do not reject the null hypothesis.
[tex]|z| > 2.054[/tex]: Reject the null hypothesis.
b) [tex]z = 2.81[/tex]
c) Reject.
d) The p-value is 0.005.
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and the subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Population 1:
Sample of 42, standard deviation of 3.3, mean of 101, so:
[tex]\mu_1 = 101[/tex]
[tex]s_1 = \frac{3.3}{\sqrt{42}} = 0.51[/tex]
Population 2:
Sample of 53, standard deviation of 3.6, mean of 99, so:
[tex]\mu_2 = 99[/tex]
[tex]s_2 = \frac{3.6}{\sqrt{53}} = 0.495[/tex]
H0 : μ1 = μ2
Can also be written as:
[tex]H_0: \mu_1 - \mu_2 = 0[/tex]
H1 : μ1 ≠ μ2
Can also be written as:
[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error .
a. State the decision rule.
0.04 significance level.
Two-tailed test(test if the means are different), so between the 0 + (4/2) = 2nd and the 100 - (4/2) = 98th percentile of the z-distribution, and looking at the z-table, we get that:
[tex]|z| < 2.054[/tex]: Do not reject the null hypothesis.
[tex]|z| > 2.054[/tex]: Reject the null hypothesis.
b. Compute the value of the test statistic.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the samples:
[tex]X = \mu_1 - \mu_2 = 101 - 99 = 2[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.51^2 + 0.495^2} = 0.71[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{2 - 0}{0.71}[/tex]
[tex]z = 2.81[/tex]
c. What is your decision regarding H0?
[tex]|z| = 2.81 > 2.054[/tex], which means that the decision is to reject the null hypothesis.
d. What is the p-value?
Probability that the means differ by at least 2, either plus or minus, which is P(|z| > 2.81), which is 2 multiplied by the p-value of z = -2.81.
Looking at the z-table, z = -2.81 has a p-value of 0.0025.
2*0.0025 = 0.005
The p-value is 0.005.
A plane flying horizontally at an altitude of 3 mi and a speed of 460 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 4 mi away from the station (Round your answer to the nearest whole number.) 368 X mi/h Enhanced Feedback Please try again. Keep in mind that distance - (altitude)2 + (horizontal distance)? (or y = x + n ). Differentiate with respect to con both sides of the equation, using the Chain Rule, to solve for the given speed of the plane is x.
Answer:
[tex]\frac{dy}{dt}=304mi/h[/tex]
Step-by-step explanation:
From the question we are told that:
Height of Plane [tex]h=3mi[/tex]
Speed [tex]\frac{dx}{dt}=460mi/h[/tex]
Distance from station [tex]d=4mi[/tex]
Generally the equation for The Pythagoras Theorem is is mathematically given by
[tex]x^2+3^2=y^2[/tex]
For y=d
[tex]x^2+3^2=d^2[/tex]
[tex]x^2+3^2=4^2[/tex]
[tex]x=\sqrt{7}[/tex]
Therefore
[tex]x^2+3^2=y^2[/tex]
Differentiating with respect to time t we have
[tex]2x\frac{dx}{dt}=2y\frac{dy}{dt}[/tex]
[tex]\frac{dy}{dt}=\frac{x}{y}\frac{dx}{dt}[/tex]
[tex]\frac{dy}{dt}=\frac{\sqrt{7}}{4} *460[/tex]
[tex]\frac{dy}{dt}=304.2614008mi/h[/tex]
[tex]\frac{dy}{dt}=304mi/h[/tex]
salifye pizza charges a base pizza of $12.77 for large plus 7.44 additional topping.
a) Find a function that models the price of a pizza with toppings.
Find the inverse of the function. What does−1 represent?
If a pizza costs $20.20, how many toppings does it have?
Answer:
Sharjah Call Girls +971529238486 | Call Girls In Sharjah
Step-by-step explanation:
Sharjah Call Girls and our group are very a good deal satisfied to participate withinside the boom of the leisure field. Lots of customers are touring Sharjah now no longer handiest for playing the splendor of the town however additionally to the sensual entertainments our profiles.
Find the distance of the point (4,4,−4) from the line r(t)=⟨−1+2t,1+2t,3−3t⟩.
Translate the given point and line together so that you get a new point and a new line that passes through the origin. This turns the problem into finding the distance between the new point,
p = (4, 4, -4) - (-1, 1, 3) = (5, 3, -7)
and the new line,
r*(t) = r(t) - ⟨-1, 1, 3⟩ = ⟨2t, 2t, -3t⟩
Let p = ⟨5, 3, -7⟩, the vector starting at the origin and pointing to p. Then the quantity ||p - r*(t)|| is the distance from the point p to the line r*(t).
Let u be such that ||p - r*(t)|| is minimized. At the value t = u, the vector p - r*(t) is orthogonal to the line r*(t), so that
(p - r*(u) ) • r*(u) = 0
I've attached a sketch with all these elements in case this description is confusing. (The red dashed line is meant to be perpendicular to r*(t).)
Solve this equation for u :
p • r*(u) - r*(u) • r*(u) = 0
p • r*(u) = r*(u) • r*(u)
and x • x = ||x||² for any vector x, so
p • r*(u) = ||r*(u)||²
⟨5, 3, -7⟩ • ⟨2u, 2u, -3u⟩ = (2u)² + (2u)² + (-3u)²
10u + 6u + 21u = 4u ² + 4u ² + 9u ²
17u ² - 37u = 0
u (17u - 37) = 0
==> u = 0 or u = 37/17
We ignore u = 0, since the dot product of any vector with the zero vector is 0.
Then the minimum distance distance between the given point and line is
||p - r*(u)|| = ||⟨5, 3, -7⟩ - 37/17 ⟨2, 2, -3⟩|| = √(42/17)
[tex]Solve. Clear fraction first.6/5 + 2/5 x = 89/30 + 7/6 x + 1/6[/tex]
Step-by-step explanation:
we have denominators 5, 6 and 30.
the smallest number that is divisible by all 3 is clearly 30.
so, we have to multiply everything by 30 to eliminate the fractions.
180/5 + 60/5 x = 89 + 210/6 x + 30/6 =
36 + 12x = 89 + 35x + 5
-58 = 23x
x = -58/23
In an interview for a secretary position at the dealer, a typist claims a tying speed of 45 words per minute. On
On the basis of 70 trials, she demonstrated an average speed of 43 words per minute with a standard deviation of 15 words per minute.
Test at 5% significance level on the typist’s claim.
Using the hypothesis test for one sample mean, There is NO SIGNIFICANT EVIDENCE to support the typist's claim
[tex]H_{0} = 45\\H_{1} < 45\\\\[/tex]
The test statistic :
T = (x - μ) ÷ (s/√(n))
T = (43 - 45) ÷ (15/√70)
T = - 2 ÷ 1.7928429
T = -1.12
At α = 0.05
Pvalue :
Degree of freedom, df = 70 - 1 = 69
Pvalue = 0.1333
Decision region :
Reject [tex]H_{0}[/tex] if Pvalue < α
0.1333 > 0.05
Since Pvalue > α We fail to reject the Null
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a day? 6. If 18 pumps can raise 2150 tonnes of water in 50 days, working 8 hours a day, how much water will be raised in 60 days by 16 out of which 10 are working 9 hours a day and the rest 7 hours a day?
please help me with this
Evaluate -8 × |2|.
Answer:
-16
Step-by-step explanation:
The absolute value of 2 is 2 so -8*2=-16
find the surface area of the prism HURRY
Answer:
Does the answer help you?
I need help ASAP please and thank you
9514 1404 393
Answer:
C. 4 +√(x+5)
Step-by-step explanation:
The sign between the terms changes to form the conjugate. The radical contents are unchanged.
The conjugate of 4 -√(x+5) is 4 +√(x+5).
_____
Additional comment
The utility of a conjugate is that the product of a number and its conjugate is the difference of two squares. The squares are intended to remove an undesirable feature of the number, its imaginary part or its irrational part, for example. Here, the product of the number and its conjugate would be ...
(a -b)(a +b) = a² -b²
4² -(√(x+5))² = 16 -(x +5) = 11 -x . . . . no longer contains a root
What is the slope of the line through (-9,6)(−9,6)left parenthesis, minus, 9, comma, 6, right parenthesis and (-6,-9)(−6,−9)left parenthesis, minus, 6, comma, minus, 9, right parenthesis?
Answer:
Step-by-step explanation:
Slope of line through (-9,6) and (-6,-9) = (-9 - 6)/(-6 - (-9)) = (-15)/(3) = -5
point-slope equation for line of slope -5 that passes through (-9,6):
y-6 = -5(x+9)
Answer:
1/2
Step-by-step explanation:
because i answered it on khan academy and it was right
Slope=
Run
Rise
=
Change in x
Change in y
start text, S, l, o, p, e, end text, equals, start fraction, start text, R, i, s, e, end text, divided by, start text, R, u, n, end text, end fraction, equals, start fraction, start text, C, h, a, n, g, e, space, i, n, space, end text, y, divided by, start text, C, h, a, n, g, e, space, i, n, space, end text, x, end fraction
Hint #22 / 3
\begin{aligned} \text{Slope}&=\dfrac{9-6}{-3-(-9)} \\\\ &=\dfrac{3}{6} \\\\ &=\dfrac{1}{2} \end{aligned}
Slope
=
−3−(−9)
9−6
=
6
3
=
2
1
Hint #33 / 3
The slope is \dfrac{1}{2}
2
1
start fraction, 1, divided by, 2, end fraction.
Which of the following would increase the width of a confidence interval for a population mean? Choose the correct answer below. A. Increase the level of confidence B. Decrease the sample standard deviation. C. Increase the sample size D. All of the above
Answer:
A. Increase the level of confidence
Step-by-step explanation:
The margin of error is given by:
The margin of error is:
[tex]M = \frac{Ts}{\sqrt{n}}[/tex]
In which T is related to the level of confidence(the higher the level of confidence, the higher T is), s is the standard deviation of the sample and n is the size of the sample.
Increase the width:
That is, increasing the margin of error, as the width is twice the margin of error, the possible options are:
Increase T -> increase confidence level.
Increase s -> Increase the standard deviation of the sample.
Decrease n -> Decrease the sample size.
Thus, the correct answer is given by option A.
Please help me! I need answer asap
Answer:
1/10
Step-by-step explanation:
1/5*1/2
1/10
Write the English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. Six times the sun of 4 and a number
Answer:
6x + 24
Step-by-step explanation:
6 * (4 + x) = 6 * 4 + 6 * x = 6x + 24
kabura bought a piece of cloth 3 metres long. The material shrunk by 1% after washing. What was the new length of the cloth
Answer:
2.97m
Step-by-step explanation:
1% of 3m =1/100×3=0.03
0.03m of cloth was shrunk,
So, New lenght : 3-0.03=2.97m
Find the slope of the line passing through the points (-1, 7) and (-5, 1)
Answer:
3/2
Step-by-step explanation:
y2 - y1 / x2 - x1
1 - 7 / -5 - (-1)
-6 / -4
= 3/2
Answer:
m=3/2
Step-by-step explanation:
m=y2-y1/x2-x1
m=1-7/-5-(-1)
m=-6/-4
m=3/2
b) solve by factorisation
[tex]x { }^{2} + x - 72 = 0[/tex]
QUESTION:- SOLVE EQUATION BY FACTORISATION
EQUATION:-
[tex] {x}^{2} + x - 72 = 0[/tex]
ANSWER:-
[tex] {x}^{2} + x - 72 = 0\\{x}^{2} + 9x - 8x - 72 = 0 \\ x(x + 9) - 8(x +9) = 0 \\ (x - 8)(x + 9) = 0 \\ [/tex]
NOW FOR VALUE OF X ->
[tex]x - 8 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x + 9 = 0\\ x = 8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = - 9[/tex]
The math teacher and cheerleading coach have teamed up to help the students do better on their math test. The cheer coach, using dance move names for the positioning of their arms, yells out polynomial functions with different degrees.
For each position the coach yells out, write the shape by describing the position of your left and right arm.
a1. Constant Function:
a2. Positive Linear Function:
a3. Negative Linear Function:
a4. Positive Quadratic Function:
a5. Negative Quadratic Function:
a6. Positive Cubic Function:
a7. Negative Cubic Function:
a8. Positive Quartic Function:
a9. Negative Quartic Function:
When it comes time to take the test not only do the students have to describe the shape of the polynomial function, you have to find the number of positive and negative real zeros, including complex. Use the equation below:
[tex]f(x)=x^5-3x^4-5x^3+5x^2-6x+8[/tex]
b. Identify all possible rational zeros.
c. How many possible positive real zeros are there? How many possible negative real zeros? How many possible complex zeros?
d. Graph the polynomial to approximate the zeros. What are the rational zeros? Use synthetic division to verify these are correct.
e. Write the polynomial in factor form.
f. What are the complex zeros?
Step-by-step explanation:
a1. The shape will be a vertical or horizontal line.
a2. The shape will be shaped like a diagonal line increasing as we go right.
a3. The shape will be shaped like a diagonal line decreasing as we go right.
a4. The shape will be shaped like a U facing upwards.
a5.The shape will be shaped like a U facing downwards.
a6. The shape will look like a S shape and it increases as we go right.
a7. The shape will look like a S shape and it decreases as We go right.
a8. The shape look like a W shape and it facing upwards.
a9. The shape look a W shape facing downwards.
We are given function.
[tex]x {}^{5} - 3x {}^{4} - 5x {}^{3} + 5x {}^{2} - 6x + 8[/tex]
b. We can test by the Rational Roots Test,
This means a the possible roots are
plus or minus(1,2,4,8).
c. If we apply Descrates Rule of Signs,
There are 3 possible positive roots or 1 possible positive root.There are also 1 possible negative root.There is also 1 possible complex root.d. Use Desmos to Graph the Function. Some roots are (-2,1,4).
e.
[tex](x {}^{2} + 1) (x - 1)(x - 4)(x + 2)[/tex]
f. The complex zeroes are
i and -i
Polynomial [tex]f(x) = x^{5} -3x^{4} - 5x^{3} + 5x^{2} - 6x + 8[/tex] in factor form: (x-1)(x+2)(x-4)(x-i)(x+i)
What is a polynomial?A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Shape of the graph for the following polynomial:
Constant function - straight line parallel to x axis.Positive linear function - straight line slanting upwards from left to right.Negative linear function - straight line slanting downwards from left to right.Positive quadratic function - U shaped curve opening upwardsNegative quadratic function - U shaped curve opening downwardsPositive cubic function - right hand curved upwards, left hand curved downwards.Negative cubic function - Left hand curved upwards, right hand curved downwards. Positive quartic function - W shaped facing upwardsNegative quartic function - W shaped facing downwardsFinding zeros of the polynomial given:
[tex]f(x) = x^{5} -3x^{4} - 5x^{3} + 5x^{2} - 6x + 8[/tex]
By factor theorem, if f(t) = 0, t is a zero of the polynomial.
Taking t = 1.
f(1) = 1 - 3 - 5 + 5 - 6 + 8 = 0
(x - 1) is a factor of the polynomial f(x).
Divide f(x) by (x-1) using long division to find the other factors.
f(x)/(x-1) = [tex]x^{4} -2x^{3}-7x^{2} -2x-8[/tex] is also a factor of f(x).
Factorizing it further:
g(x) = [tex]x^{4} -2x^{3}-7x^{2} -2x-8[/tex]
g(-2) = 16 + 16 - 28 + 4 - 8 = 0
(x + 2) is a factor of g(x) and thus f(x).
g(x)/(x+2) = [tex]x^{3} - 4x^{2} +x - 4[/tex] is a factor of f(x).
Factorizing it further:
k(x) = [tex]x^{3} - 4x^{2} +x - 4[/tex]
k(4) = 64 - 64 + 4 - 4 = 0
(x - 4) is a factor of k(x) thus of f(x).
k(x)/(x-4) = [tex]x^{2} +1[/tex]
Factorizing it further:
l(x) = [tex]x^{2} +1[/tex] = (x + i)(x - i)
Zeros of f(x) = 1, -2, 4, ±i
Rational zeros : 1, -2, 4
Positive real zeros: 1, 4
Negative real zeros: -2
Complex zeros: ±i
Polynomial in factor form: (x-1)(x+2)(x-4)(x-i)(x+i).
Learn more about polynomial here
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if a gallon of milk costs $2.49 how much will 3 1/2 gallons cost
did from six times a certain number the result is 96 what is the number
Answer:
The number is 16
Step-by-step explanation:
Number : x
Procedure and resolution:
6x = 96
x = 96/6
x = 16
Good Luck!Greatest to least just need some help will help ty(please don’t give wrong answer)
Answer:
try 91.78, 91.58, 91.26, 363.4
Step-by-step explanation:
Question 24 plz show ALL STEPS
9514 1404 393
Answer:
see attached
Step-by-step explanation:
a) The first 5 partial sums are listed in the table in the attachment.
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b) Sigma notation makes use of the general term shown:
[tex]\displaystyle\sum_{n=1}^\infty{\frac{3^n+(-2)^n}{6^n}}[/tex]
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c) The sum appears to be close to 3/4. (For large n, a calculator cannot evaluate the terms of the series--they are too small.) The attachment shows the 100th sum to be rounded to 3/4 (from 12 significant digits).
